Green’s Dictionary of Slang

fiddle (and flute) n.

(US) a suit.

1919		T.A. Dorgan in Zwilling TAD Lex. (1993) 36: Its the rhyming slang. Fiddle and flute that’s a suit.
1928		M.C. Sharpe Chicago May: Her Story in Hamilton (1952) 132: Fiddle and flute – suit.
1935		A.J. Pollock Und. Speaks.
1946		St. Vincent Troubridge ‘Some Notes on Rhyming Argot’ in AS XXI:1 Feb. 46: fiddle and flute or fiddle. A suit of clothes. (Origin uncertain, but probably English.) Agreed as English, but always whistle and flute. The word fiddle alone has its own slang meaning, especially as a verb, viz., to obtain by illicit means, generally including bribery or petty crime. Very near the American ‘graft.’.
1949		Monteleone Criminal Sl. (rev. edn).
1963		M. Braly Shake Him Till He Rattles (1964) 106: ‘Where’d you get the hairy fiddle?’ Cabiness pulled at the front of his new suit coat.
1991		(con. 1920s) O.D. Brooks Legs 225: You can get slicked up in your new fiddle.
1999		R. Walton ‘Cockney Jack’ 🌐 He got up and put on his throw me in the dirt, his wool fiddle and flute, his Jack-in-the-box and his daisy roots.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.